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Curved Space

Nicholas Manton and Nicholas Mee

in The Physical World: An Inspirational Tour of Fundamental Physics

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198795933
eISBN:
9780191837111
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198795933.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops the mathematical technology required to understand general relativity by taking the reader from the traditional flat space geometry of Euclid to the geometry of Riemann that ... More


Exploring the Sphere

Glen Van Brummelen

in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175997
eISBN:
9781400844807
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175997.003.0002
Subject:
Mathematics, History of Mathematics

This chapter introduces the reader to the celestial sphere, or the Earth's surface. By rotating the sphere, the motions of the heavens can be simulated. There are three features of celestial motion ... More


A framework toward understanding the characterization of holomorphic dynamics

Yunping Jiang

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reviews the characterization of geometrically finite rational maps and then outlines a framework for characterizing holomorphic maps. Whereas Thurston's methods are based on estimates of ... More


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